CFD modeling of gas dispersion and bubble size in a double turbine stirred tank

In the present paper, gas dispersion in a double turbine baffled stirred tank is modeled using a commercial computational fluid dynamics (CFD) code FLUENT 6.1 (Fluent Inc., USA). A bubble number density equation is implemented in order to account for the combined effect of bubble break-up and coalescence in the tank. In the proposed work, the impellers are explicitly described in three dimensions using multiple reference frame model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-ε turbulent model and modified standard drag coefficient for the momentum exchange. The model predicts spatial distribution of gas holdup, average local bubble size and flow structure. The results are compared with experimental and numerical finding reported in the literature and good agreement between the present model and measurements of Alves et al. [Gas liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering Science, 2002, 57, 487-496] is achieved.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Estimation of kLa Values in Bench‐Scale Stirred Tank Reactors with Self‐Inducing Impeller by Multiphase CFD Simulations

A multiphase computational fluid dynamics (CFD) simulation methodology is developed and proposed for the estimation of the spatial distribution of k_La values in a bench‐scale reactor equipped with a self‐inducing impeller. The importance of estimating an apparent drag coefficient, which considers the effect of turbulence on the gas bubble rising velocity, is also tackled by applying different correlations available in literature, namely, Brucato, modified Brucato, and Pinelli correlations. The spatial distribution of k_La values in the agitated vessel is found from the CFD results using Danckwert's surface renewal model. An analysis of the gas volume fraction distribution obtained from the simulations is performed in order to choose the most suitable drag model. The modified Brucato correction correlation for the drag force exhibits the best agreement with experimental data.     

Experimental and modelling study of gas dispersion in a double turbine stirred tank

Gas dispersion in a double turbine stirred tank is experimentally characterised by measuring local gas holdups and local bubble size distributions throughout the tank, for three liquid media: tap water, aqueous sulphate solution and aqueous sulphate solution with PEG. For all these media, bubble coalescence generally prevails over breakage. Where average bubble size decreases, this can be attributed to the difference in slip velocity between different sized bubbles. Most of the coalescence takes place in the turbine discharge stream.A compartment model that takes into account the combined effect of bubble coalescence and breakage is used to simulate gas dispersion. The model predicts spatial distribution of gas holdup and of average bubble size, with average bubble size at the turbines as an input. Reasonable agreement between experiment and simulation is achieved with optimisation of two parameters, one affecting mainly the slip velocity, the other related mainly to the bubble coalescence/breakage balance. Different sets of parameters are required for each of the three liquid systems under study, but are independent of stirring/aeration conditions. The model only fails to simulate the smaller average bubble diameters at the bottom of the tank.     

Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels

Suspensions of solid particles into liquids within industrial stirred tanks are frequently carried out at an impeller speed lower than the minimum required for complete suspension conditions. This choice allows power savings which usually overcome the drawback of a smaller particle-liquid interfacial area. Despite this attractive economical perspective, only limited attention has been paid so far to the modelling of the partial suspension regime.     

Prediction of the Induced Gas Flow Rate from a Self‐Inducing Impeller with CFD

The complex task of describing computationally two‐phase turbulent flows in aerated stirred‐tank reactors was overcome by proposing that the gas flow rate in the hollow impeller can be estimated from single‐phase flow simulations of the liquid phase in the reactor: the pressure at the impeller surface obtained from liquid phase simulations can be related to the gas induction rate. A commercial lab‐scale reactor with a radial six‐bladed hollow impeller was chosen for the study. To validate the presented methodology, the induced gas flow rate was measured experimentally from the tracking of the position of bubbles in a dynamic sequence of flow images. Notwithstanding the simplifications assumed in the presented CFD methodology, good agreement has been obtained between numerical results and experiments.     

CFD simulation of flow and mixing characteristics in a stirred tank agitated by improved disc turbines

To reduce the power consumption and improve the mixing performance in stirred tanks, two improved disc turbines namely swept-back parabolic disc turbine (SPDT) and staggered fan-shaped parabolic disc turbine (SFPDT) are developed. After validation of computational fluid dynamics (CFD) model with experimental results, CFD simulations are carried out to study the flow pattern, mean velocity, power consumption, pumping capacity and mixing efficiency of the improved and traditional impellers in a dished-bottom tank under turbulent flow conditions. The results indicate that compared with the commonly used parabolic disc turbine (PDT), the power number of proposed SPDT and SFPDT impellers is reduced by 43% and 12%, and the pumping efficiency is increased by 68% and 13%, respectively. Furthermore, under the same power consumption (0-700 W·m^-3), the mixing performance of both SPDT and SFPDT is also superior to that of Rushton turbine and PDT.     

Assessment of large eddy and RANS stirred tank simulations by means of LDA

Large eddy simulations (LES) and Reynolds-averaged Navier-Stokes (RANS) calculations were performed on the flow in a baffled stirred tank, driven by a Rushton turbine at Re=7300. The LES methodology provides detailed flow information as velocity fluctuations are resolved down to the scale of the numerical grid. The Smagorinsky and Voke subgrid-scale models used in the LES were embedded in a numerical lattice-Boltzmann scheme for discretizing the Navier-Stokes equations, and an adaptive force-field technique was used for modeling the geometry. The uniform, cubic computational grid had a size of 240³ grid nodes. The RANS calculations were performed using the computational fluid dynamics code CFX 5.5.1. A transient sliding mesh procedure was applied in combination with the shear-stress-transport (SST) turbulence closure model. The mesh used for the RANS calculation consisted of 241464 nodes and 228096 elements (hexahedrons). Phase-averaged and phase-resolved flow field data, as well as turbulence characteristics, based on the LES and RANS results, are compared both mutually and with a single set of experimental data.     

Measurement of phase holdups in liquid-liquid-solid three-phase stirred tanks and CFD simulation

Phase holdup is an important hydrodynamic characteristic of multiphase systems relevant to optimization and scale-up of related process equipment. In the present article, measurements of phase distribution of solid particles and oil droplets are conducted in a lab-scale stirred tank by sample withdrawal under various operating conditions. A Eulerian-Eulerian three-fluid model is established for the prediction of phase distribution of two dispersed phases in the agitated liquid-liquid-solid dispersion system. The turbulence structure in the system is described by an extension of the standard k-ε turbulence model to three-phase flow including the influence of presence of two dispersed phases as an additional source of turbulent kinetic energy. Momentum exchange between continuous and dispersed phase as well as between the two dispersed phases are incorporated into the model formulation. Comparison of model predictions with experimental data suggests reasonable agreement for the dispersed oil phase. The predicted distribution of solid particles shows some discrepancies in comparison with the measurements, but the agreement is significantly improved for higher impeller speeds.     

双层涡轮桨搅拌反应器内混合时间的大涡模拟

采用计算流体力学(CFD)方法对直径为0.476m双层涡轮桨搅拌反应器内的流动及混合进行了数值模拟,并实验测试了混合过程。利用大涡模拟(LES)及Smagorinsky-Lilly亚格子模型求解湍流流动与示踪剂传递过程,桨叶区域采用滑移网格技术。研究结果表明,大涡模拟得到的示踪剂响应曲线和混合时间与实验结果吻合良好,其预测精度明显优于基于雷诺平均(Reynolds-averaged Navier-Stokes,RANS)的标准k-ε模型的模拟结果。大涡模拟是研究搅拌反应器内非稳态及周期性湍流流动的有效方法。     

Scalar mixing in a turbulent stirred tank with pitched blade turbine: Role of impeller speed perturbation

Mixing of a passive scalar inside a pitched blade turbine (PBT) impeller stirred tank (STR) is studied using large-eddy simulation (LES) coupled with the immersed boundary method (IBM) for resolving moving interfaces. Mixing time is calculated based on the 95% homogenization of the scalar over the entire tank volume. Growth rate of the unmixed tracer volume is observed in order to identify the effects of low frequency macroinstability (MI) oscillations. Mixing time is significantly reduced when the STR flow is perturbed using a step-change in the impeller speed with a specific MI frequency. The enhancement in turbulent kinetic energy and changes in mean flow field due to the perturbation is observed. The spatio-temporal behavior of the large-scale mixing structures for the fixed impeller-speed case and the perturbed case are compared. The mechanism of mixing enhancement is further explored by observing dynamic changes in the concentration distribution and the velocity field over a perturbation cycle. Penalty in power requirement due to perturbation is calculated.     

搅拌槽中酯化反应热失控的CFD模拟

热失控是化工过程中常见的安全风险之一。在间歇釜式反应器中,桨叶的机械转动可以增强流体的循环流动、湍流强度、混合程度以及传热,进而有效防范热失控。防控效果与反应器结构和搅拌桨型密切相关。针对丙酸异丙酯酯化反应,采用计算流体力学模拟研究了桨型(Rushton桨、30o PBT桨及60o PBT桨)、转动方向和挡板对釜式反应器内温度演化的影响,从流动结构方面分析了原因。基于散度的失控判据比较了三种搅拌桨抑制热失控的能力,抑制能力为Rushton桨＞30° PBTD桨＞60° PBTD桨。本研究可为搅拌反应器热失控的优化设计提供一定的理论依据。     

STUDY OF THE TURBULENT FLOW IN AN UNBAFFLED STIRRED TANK BY DETACHED EDDY SIMULATION

Detached eddy simulation (DES) of the liquid-phase turbulent flow in an unbaffled stirred tank agitated by a six-blade, 45°-pitched blade turbine was performed in this study. The tank wall is cylindrical with no baffle and the fluid flow problem was solved in a single reference frame (SRF) rotating with the impeller. For the purpose of comparison, computation based on large eddy simulation (LES) was also carried out. The commercial code Fluent was used for all simulations. Predictions of the phase-averaged turbulent flow quantities and power consumption were conducted. Results obtained by DES were compared with experimental laser Doppler velocimetry (LDV) data from the literature and with the predictions obtained by LES. It was found that numerical results of mean velocity and turbulent kinetic energy profiles as well as the power consumption are in good agreement with the LDV data. When performed on the same computational grid, which is under-resolved in the sense of LES, DES allows better accuracy than LES in that it works better in the boundary layers on the surface of the impeller and the stirred tank walls. It can be concluded that DES has the potential to predict accurately the turbulent flow in stirred tanks and can be used as an effective tool to study the hydrodynamics in stirred tanks.     

Numerical simulation of a dissolution process in a stirred tank reactor

A dissolution process of solid particles suspended in a turbulent flow of a Rushton turbine stirred tank is studied numerically by large eddy simulations including passive scalar transport and particle tracking. The lattice-Boltzmann flow solver and the Smagorinsky subgrid-scale model are adopted for solving the stirred tank flow. To the LES a finite volume scheme is coupled that solves the convection-diffusion equation for the solute. The solid particles are tracked in the Eulerian flow field through solving the dynamic equations of linear and rotational motion of the particles. Particle-particle and particle-wall collisions are included, and the particle transport code is two-way coupled. The simulation has been restricted to a lab-scale tank with a volume equal to . A set of 7×10⁶ spherical particles in diameter are released in the top part of the tank (10% of the tank volume), resulting in a local initial solids volume fraction of 10%. The particle properties are such that they resemble those of calcium chloride beads. The focus is on solids and scalar concentration distributions, particle size distributions, and the dissolution time. For the particular process considered, the dissolution time is found to be at most one order of magnitude larger than the time needed to fully disperse the solids throughout the tank.     

Effect of pitched short blades on the flow characteristics in a stirred tank with long-short blades impeller

This work focuses on the design improvement of the long-short blades (LSB) impeller by using pitched short blades (SBs) to regulate the flow field in the stirred vessel. After mesh size evaluation and velocity field validation by the particle image velocimetry, large eddy simulation method coupled with sliding mesh approach was used to study the effect of the pitched SBs on the flow characteristics. We changed the inclined angles of the SBs from 30° to 60° and compared the flow characteristics when the impeller was operated in the down-pumping and up-pumping modes. In the case of down-pumping mode, the power number is relatively smaller and vortexes below the SBs are suppressed, leading to turbulence intensification in the bottom of the vessel. Whereas in the case of up-pumping mode, the axial flow rate in the center increased significantly with bigger power number, resulting in more efficient mass exchange between the axial and radial flows in the whole vessel. The LSB with 45° inclined angle of the SBs in the up-pumping mode has the most uniform distributions of flow field and turbulent kinetic energy compared with other impeller configurations.     

CFD simulations of two stirred tank reactors with stationary catalytic basket

Among the different systems used for laboratory kinetic investigation, stationary catalytic basket stirred tank reactors (SCBSTRs) allow one to study triphasic reactions involving shaped catalyst with large size. The hydrodynamics of these complex reactors is not well known and has been studied experimentally in only a few cases. Despite the difference in the design of two commercial SCBSTRs reported in these works, the local measurements of the liquid-solid mass transfer coefficient inside the catalytic basket revealed the same velocity profile. The aim of the present work is therefore to investigate more accurately the hydrodynamics of the two reactors by means of CFD in order to compare the effect of the blade/baffle hydrodynamic interaction on the flow pattern. Owing to the geometrical complexity of the reactors, the hydrodynamic investigation is based on the k-ε model and the Brinkman-Forsheimer equations. The agreement at the local level with the experimental data (PIV and mass transfer measurements) validates this preliminary work performed with the standard values of the parameters present in the turbulent model and the Brinkman-Forsheimer equations. The simulations reveal in both reactors a ring-shaped vortex around the impeller in the agitation region. The high axial location of its centre induces a reverse flow at the tips of the basket. Owing to the fluid friction in the porous medium, the azimuthal flow in the core region is transformed into a radial flow in the basket where the flow decreases abruptly. Vertical vortices are located at the blade tips and at the downstream face of the baffles or they are located in the basket on both sides of the baffles, depending on the design and the location of the baffles. At the inner radius interface of the basket, the vertical blade impeller induces a rather homogeneous velocity profile, but the pitched blade impeller imposes a high velocity at the plane of symmetry. Therefore the simulations demonstrate that two different local velocity patterns and two different porous media may induce the same mass transfer properties.     

Validation of CFD simulations of a stirred tank using particle image velocimetry data

Methods for validating CFD simulations based on the Reynolds Average Navier-Stokes equation (RANS) against Particle Image Velocimetry (PIV) measurements are investigated and applied to one of the most common problems in the chemical process industry — the prediction of flow field in a stirred vessel. A total of 1024 sequential instantaneous 2D velocity fields along the central axial plane of a stirred vessel with a P-4 axial impeller are obtained through PIV measurement. From the PIV data, the mean velocity, turbulent kinetic energy, Reynolds stresses and dissipation rate fields are extracted. By introducing several tools to quantify the similarities and differences between two-dimensional fields, CFD predictions of the flow field are validated against PIV data. Furthermore, using PIV and LDV data, the effect of boundary conditions on CFD simulation results is examined. The effect of different Reynolds stress closures on the flow prediction is also studied.     

大涡模拟搅拌槽中的液相流动

采采用大涡模拟湍流模型对有档板的Rushton 桨搅拌槽进行了数值模拟研究。控制方程采用控制容积法进行离散,对流项用三阶QUICK格式,扩散项是二阶中心差分。压力 速度耦合方程在交错网格上采用SIMPLE算法进行求解。小尺度流动的模化采用动力学（dynamic）亚格子模型。搅拌桨与档板之间的相互作用采用改进的内外迭代法进行处理。计算结果和文献值吻合得很好。     

Numerical simulation of stirred tanks using a hybrid immersed-boundary method

Conventionally, multiple reference frame (MRF) method and sliding mesh (SM) method are used in the simulation of stirred tanks, however, both methods have limitations. In this study, a hybrid immersed-boundary (IB) technique is developed in a finite difference context for the numerical simulation of stirred tanks. IBs based on Lagrangian markers and solid volume fractions are used for moving and stationary boundaries, respectively, to achieve optimal efficiency and accuracy. To cope with the high computational cost in the simulation of stirred tanks, the technique is implemented on computers with hybrid architecture where central processing units (CPUs) and graphics processing units (GPUs) are used together. The accuracy and efficiency of the present technique are first demonstrated in a relatively simple case, and then the technique is applied to the simulation of turbulent flow in a Rushton stirred tank with large eddy simulation (LES). Finally the proposed methodology is coupled with discrete element method (DEM) to accomplish particle-resolved simulation of solid suspensions in small stirred tanks. It demonstrates that the proposed methodology is a promising tool in simulating turbulent flow in stirred tanks with complex geometries.